Multiple DGs for Reducing Total Power Losses in Radial Distribution Systems Using Hybrid WOA-SSA Algorithm

Table 7

Performance of WOA-SSA compared with those of the WOA and SSA algorithms and the IEEE case without DG on an IEEE 123-bus RDN with multiple DGs.

DG no.	Particulars	Base case without DG	Algorithms
			WOA	SSA	WOA-SSA
3	Candidate buses	—	90, 28, 160	149, 56, 97	152, 45, 67
	Optimal DG size (kW)	—	5000; 3822.095; 1826.522	755.84; 1558.834; 1667	1745.644; 2642.309; 1995.555
	Total DG size (kW)	—	10648.617	3981.674	6383.508
	Total power losses (kW)	95.434	70.696	70.978	70.292
	% power loss reduction	—	25.9%	25.6%	26.4%
	Minimum voltage (p.u.), Bus	0.98401, 65	0.98791, 65	0.98948, 65	0.97858, 65
	Maximum voltage (p.u.), Bus	1.0481, 83	1.0463, 83	1.0476, 83	1.0403, 83
	Mean voltage (p.u.)	1.0207	1.0209	1.0209	1.0152
	Standard deviation voltage (p.u.)	0.018416	0.014141	0.015043	0.014254
	Computational time (S)	—	231	224	228
4	Candidate buses	—	52, 51, 25, 54	52, 42, 250, 54	13, 51, 36, 57
	Optimal DG size (kW)	—	4491.045; 2109.597; 2126.813; 2034.666	1657.875; 2089.409; 3275.819; 2146.397	488.383; 1160.717; 2568.928; 2479.022
	Total DG size (kW)	—	10762.121	9169.5	6697.05
	Total losses (kW)	95.434	74.238	73.969	73.091
	% loss reduction	—	22.2%	22.5%	23.4%
	Minimum voltage (p.u.), bus	0.98401, 65	0.98234, 65	0.98097, 65	0.97407, 65
	Maximum voltage (p.u.), bus	1.0481, 83	1.0446, 83	1.0436, 83	1.0458, 83
	Mean voltage (p.u.)	1.0207	1.0135	1.013	1.0123
	Standard deviation voltage (p.u.)	0.018416	0.019012	0.01825	0.017625
	Computational time (S)	—	278	284	274
5	Candidate buses	—	81, 48, 149, 23, 67	55, 26, 56, 40, 57	78, 98, 61, 29, 67
	Optimal DG size (kW)	—	2686.689; 2003.240; 2039.694; 1336.645; 1770.532	38.473; 589.953; 4572.243; 397.187; 2016.337	1599.443; 3560.55; 1557.516; 4062.252; 1899.762
	Total DG size (kW)	—	9836.8	7614.193	12679.523
	Total power losses (kW)	95.434	70.635	72.928	70.184
	% power loss reduction	—	26%	23.6%	26.5%
	Minimum voltage (p.u.), bus	0.98401, 65	0.97585, 65	0.98545, 65	0.97991, 65
	Maximum voltage (p.u.), bus	1.0481, 83	1.0412, 83	1.0468, 83	1.0453, 83
	Mean voltage (p.u.)	1.0207	1.0117	1.0171	1.0159
	Standard deviation voltage (p.u.)	0.018416	0.016813	0.016408	0.015152
	Computational time (S)	—	237	255	232
6	Candidate buses	—	26, 28, 13, 10, 51, 53	8, 9, 35, 42, 250, 53	150, 35, 54, 13, 54, 54
	Optimal DG size (kW)	—	2457.965; 2806.089; 1605.001; 1912.286; 2838.475; 2261.193	4565.555; 258.574; 1393.951; 3839.614; 1837.754; 2789.804	4447.936; 322.867; 1040.216; 191.239; 2731.592; 2236.8
	Total DG size (kW)	—	13881.009	14685.252	10970.65
	Total losses (kW)	95.434	74.061	73.937	73.419
	% loss reduction	—	22.4%	22.5%	23.1%
	Minimum voltage (p.u.), bus	0.98401, 65	0.98132, 65	0.97656, 65	0.98629, 65
	Maximum voltage (p.u.), bus	1.0481, 83	1.0432, 83	1.042, 83	1.045, 83
	Mean voltage (p.u.)	1.0207	1.0131	1.0119	1.0169
	Standard deviation voltage (p.u.)	0.018416	0.018087	0.016947	0.015978
	Computational time (S)	—	301	302	273
7	Candidate buses	—	36, 97, 75, 104, 53, 34, 72	36, 25, 50, 27, 57, 8, 67	53, 56, 42, 64, 51, 62, 67
	Optimal DG size (kW)	—	2391.085; 5000; 2797.53; 3450.195; 5000; 4439.535; 1888.471	1; 1; 5000; 1748.772; 1; 5000; 1877.048	1966.79; 2039.543; 2147.753; 3201.916; 3603.024; 1561.412; 1926.957
	Total DG size (kW)	—	24966.816	13628.82	16447.395
	Total power losses (kW)	95.434	71.376	70.597	70.273
	% power loss reduction	—	25.2%	26%	26.4%
	Minimum voltage (p.u.), bus	0.98401, 65	0.97374, 65	0.97372, 65	0.97935, 65
	Maximum voltage (p.u.), bus	1.0481, 83	1.0479, 83	1.0448, 83	1.0458, 83
	Mean voltage (p.u.)	1.0207	1.0124	1.0131	1.0169
	Standard deviation voltage (p.u.)	0.018416	0.017836	0.018325	0.016181
	Computational time (S)	—	238	264	233
8	Candidate buses	—	36, 26, 27, 30, 29, 22, 37, 13	48, 21, 7, 51, 23, 7, 47, 57	52, 8, 20, 29, 150, 30, 1, 52
	Optimal DG size (kW)	—	2845.921; 3590.8; 3277.099; 1528.684; 1221.43; 2044.885; 2279.321; 2862.69	3731.289; 2207.028; 4943.676; 1137.604; 2771.666; 2076.816; 1761.434; 2869.06	1217.977; 1733.92; 2376.75; 181.628; 2300.277; 3794.711; 3728.088; 2376.548
	Total DG size (kW)	—	19650.83	21498.573	17709.899
	Total losses (kW)	95.434	74.856	74.363	74.071
	% loss reduction	—	21.6%	22.1%	22.4%
	Minimum voltage (p.u.), bus	0.98401, 65	0.99074, 65	0.96968, 65	0.9891, 65
	Maximum voltage (p.u.), bus	1.0481, 83	1.0465, 83	1.0443, 83	1.0485, 83
	Mean voltage (p.u.)	1.0207	1.0159	1.0139	1.0175
	Standard deviation voltage (p.u.)	0.018416	0.015319	0.018916	0.016697
	Computational time (S)	—	285	274	275
9	Candidate buses	—	23, 250, 49, 35, 18, 2, 17, 37, 52	29, 25, 54, 40, 250, 52, 149, 151, 57	17, 55, 2, 27, 44, 49, 44, 250, 57
	Optimal DG size (kW)	—	1041.278; 3539.659; 1006.816; 1515.389; 427.404; 467.085; 434.462; 479.55; 2200.006	4370.94; 4105.06; 4354.954; 5000; 2044.157; 4093.852; 3826.531; 638.685; 2427.329	2445.393; 1150.91; 68.636; 2389.231; 3098.096; 2860.186; 122.912; 2677.014; 2278.389
	Total DG size (kW)	—	11111.649	30861.508	17090.767
	Total losses (kW)	95.434	74.86	72.805	72.576
	% loss reduction	—	21.6%	23.7%	24%
	Minimum voltage (p.u.), bus	0.98401, 65	0.98417, 65	0.98069, 65	0.98257, 65
	Maximum voltage (p.u.), bus	1.0481, 83	1.0465, 83	1.0455, 83	1.0436, 83
	Mean voltage (p.u.)	1.0207	1.0128	1.0178	1.0164
	Standard deviation voltage (p.u.)	0.018416	0.018169	0.016801	0.015684
	Computational time (S)	—	278	279	276